function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
%   theta = GRADIENTDESENT(X, y, theta, alpha, num_iters) updates theta by
%   taking num_iters gradient steps with learning rate alpha

% Initialize some useful values
m = length(y); % number of training examples
J_history = zeros(num_iters, 1);
grad=0
for iter = 1:num_iters,

    % ====================== YOUR CODE HERE ======================
    % Instructions: Perform a single gradient step on the parameter vector
    %               theta.
    %
    % Hint: While debugging, it can be useful to print out the values
    %       of the cost function (computeCost) and gradient here.
    %

    for i = 1:m,
        grad = grad + (theta'*X(i,:)'-y(i))*X(i,:)';
    end
    theta = theta - (alpha/m)*grad;


    %grad = X' * (X*theta - y);
    %theta = theta - (alpha/m) * grad;

    % ============================================================

    % Save the cost J in every iteration
    J_history(iter) = computeCost(X, y, theta);

end
end